I was just wondering if you might be able to help me with this question:

Show that there is no rational number 's' such that s^2 = 3

thanks

Write where . Then . Factor into primes and into primes. The exponents of the primes of will all be even similarly with . However, will make one of the elements (i.e. ) to be odd. And therefore the two sides do not match up. An impossibility.